대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제49권3호
  • /
  • Pages.511-515
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  • 2012
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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PRIME RADICALS IN UP-MONOID RINGS

  • Cheon, Jeoung-Soo (Department of Mathematics Pusan National University) ;
  • Kim, Jin-A (Department of Mathematics Pusan National University)
  • 투고 : 2010.12.24
  • 발행 : 2012.05.31
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초록

We first show that the semiprimeness, primeness, and reducedness can go up to up-monoid rings. By these results we can compute the lower nilradicals of up-monoid rings, from which the well-known fact of Amitsur and McCoy for the polynomial rings can be extended to up-monoid rings.

키워드

참고문헌

  1. V. Camillo, C. Y. Hong, N. K. Kim, Y. Lee, and P. P. Nielsen, Nilpotent ideals in polynomial and power series rings, Proc. Amer. Math. Soc. 138 (2010), no. 5, 1607-1619. https://doi.org/10.1090/S0002-9939-10-10252-4
  2. C. Y. Hong, N. K. Kim, and Y. Lee, Extensions of McCoy's theorem, Glasg. Math. J. 52 (2010), no. 1, 155-159. https://doi.org/10.1017/S0017089509990243
  3. E. Jespersa, J. Krempa, and E. R. Puczylowski, On radicals of graded rings, Comm. Algebra. 10 (1982), 1849-1854. https://doi.org/10.1080/00927878208822807
  4. T. Y. Lam, A First Course in Noncommutative Rings, Springer-Verlag, New York, 1991.
  5. J. Lambek, On the representations of modules by sheaves of factor modules, Canad. Math. Bull. 14 (1971), 359-368. https://doi.org/10.4153/CMB-1971-065-1
  6. J. Okninski, Semigroup Algebras, Marcel Dekker, New York, 1991.
  7. D. S. Passman, The Algebraic Structure of Group Rings, Wiley, New York, 1977.
  8. A. Smoktunowicz, Polynomial rings over nil rings need not be nil, J. Algebra 233 (2000), no. 2, 427-436. https://doi.org/10.1006/jabr.2000.8451

피인용 문헌

  1. Properties of Different Prime Radicals of Rings and Modules vol.43, pp.3, 2015, https://doi.org/10.1080/00927872.2013.857237
  2. Nilradicals of the unique product monoid rings vol.16, pp.07, 2017, https://doi.org/10.1142/S021949881750133X